At the end of the last Knitwear Design 101 post I stated that all patterns have a geometric foundation or plan. The specific word for this plan is a tessellation. This is a mathematical term, but tessellation is known by a number of names depending on your background. Most people understand this as a repeated pattern, and there are many different ways of repeating a pattern.
The first thing to note is that pattern always begins with a single unit or motif. The tessellation, or repeat, specifies exactly how that unit or motif is multiplied throughout a larger area. Mathematically, this is described in terms of axes or lines of symmetry, but books on surface textiles don’t take this approach! Today I’ll talk about one type of tessellation symmetry, one that I know will be most accessible and familiar to knitters and crocheters – but also anyone else interested in surface pattern design.
The drop repeat is the most widely used method of tessellation symmetry in knitting and crochet. It can occur along a vertical axis – when most textile books will refer to it as a ‘drop’ repeat – or a horizontal axis, when it can also be referred to as a brick repeat. Mathematicians call the same thing a ‘slide’ or translation. The earliest examples of tessellation involve beautiful artefacts such as Islamic rugs and mosaic tiling, and my personal mnemonic is:
translate > trans slate > move tile.
Whichever terminology you use – translation or drop – both systems indicate that the original slate, tile or motif has moved out of the original alignment. To continue with textile terms, the presence of a drop denotes movement by a fraction of a step, NOT a whole step. Moving the motif by a whole step creates a block repeat, which resembles a simple grid and takes on a square formation. Here are some examples:
On the other hand, drop repeats take on a diagonal formation. Below are some examples of half drop repeats: a crochet one along the horizontal axis, and three knitted ones along the vertical axis.
In the case of the half drop, the motif has shifted by half its length (vertical) or half its width (horizontal). However, you can ‘drop’ by any fraction you like; below is a third drop plan, again with a square foundation:
Unfortunately I couldn’t find any third drop examples in my stash, but I hope you get the idea!
The key to success is to make sure that your original motif is divisible by the denominator of the proposed drop. That is, if you want to create a half drop repeat, the stitches or rows taken up by the motif must be divisible by 2 ( ½ ); if you want to create a third drop, the stitches or rows taken up by the motif must be divisible by 3 ( ⅓ ).
The half drop is a Very Big Deal in knitting and crochet because it creates beautiful art and solves technical problems. Here are a few you might have seen on your travels.
The diagonal lines created by half drop repeats are excellent for stranded colourwork because the fabric stress caused by colour changes is spread evenly. If you have knitted a lot of Fair Isle style designs, you’ll have noticed that diagonal lines create neater knitting, especially when long floats need to be woven in at the back. Vertical lines can look bulkier and require more attention when blocking because the cumulative stress of colour changes is in the same location on every row. Visually, this can be distracting – a bit like having turning chains of crochet motifs in the same place on each round.
In a similar way, stress is relieved for cables and lace because of cumulative decreases and twists. It’s no accident that so many lace patterns are based on the half drop. The falling leaves pattern, for example, cleverly offsets double decreases with eyelet increases; the ‘pulling in’ or axial bias at the centre of the leaf motif is offset by the expansion of the eyelet holes. At any point in the pattern, you will be knitting symmetrical opposites – as you decrease (sk2po) to form the pointed end of a leaf, you’ll be increasing (yarn over) to form the feathered fronds of another. And just in case you needed more proof, drop repeats give themselves away by their diagonal lines, which form perfect diamonds. Here’s one of the leaf patterns again for you:
The cable motif – a sneak peek from my swatch box – exemplifies the importance of half drop repeats: note how the sides of the swatch undulate according to the stress of the cable twists. It is a work in progress, but you can see that in order for this to work as a repeated pattern – as opposed to a single panel, as it is currently – I need to ensure that the thinner area containing the knot, or the widest part of the fabric – is exactly halfway along the hexagon, the narrowest part of the fabric. The tessellation will form only when these two design elements are perfectly aligned. This kind of problem solving involves rejigging the numbers, so the final motif may be slightly longer or shorter. Other relatively minor concerns like the knot can be easily worked out once the numbers are happy; there is no point in focusing on details like that until the overall structure has been confirmed, and I know exactly how many rows I have to work with when designing the knot.
If you want to have a go at creating your own knit or crochet designs, you cannot go wrong with squared paper. I will come back to tessellations again next time, but I thought that starting here instead of giving an overall snapshot of the ways in which shapes can fit together would make it easier to spot them out in the wild. Pattern is absolutely everywhere, and knowing something about how it works just makes it even more fascinating. I have crammed a lot into this post, but there’ll be even more next month! In the meantime, I hope you begin to see pattern in the same way I do 😊.